v?ErfInv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

v?ErfInv

Computes inverse error function value of vector elements.

Syntax

call vserfinv(n, a, y)
call vserfinvi(n, a, inca, y, incy)
call vmserfinv(n, a, y, mode)
call vmserfinvi(n, a, inca, y, incy, mode)
call vderfinv(n, a, y)
call vderfinvi(n, a, inca, y, incy)
call vmderfinv(n, a, y, mode)
call vmderfinvi(n, a, inca, y, incy, mode)

Include Files

mkl_vml.f90

Input Parameters

Name	Type	Description
`n`		Specifies the number of elements to be calculated.
`a`	Fortran 77: DOUBLE PRECISION for `vderfinv` , `vmderfinv`Fortran 90: REAL , INTENT(IN) for `vserfinv` , `vmserfinv`Fortran 90: DOUBLE PRECISION , INTENT(IN) for `vderfinv` , `vmderfinv`	Array that specifies the input vector `a` .
`inca` , `incy`	INTEGER, INTENT(IN)	Specifies increments for the elements of `a` and `y` .
`mode`	INTEGER(KIND=8) , INTENT(IN)	Overrides global VM mode setting for this function call. See vmlSetMode (Sets a new mode for VM functions according to the mode parameter and stores the previous VM mode to oldmode.) for possible values and their description.

Output Parameters

Name	Type	Description
`y`	Fortran 77: DOUBLE PRECISION for `vderfinv` , `vmderfinv`Fortran 90: REAL , INTENT(OUT) for `vserfinv` , `vmserfinv`Fortran 90: DOUBLE PRECISION , INTENT(OUT) for `vderfinv` , `vmderfinv`	Array that specifies the output vector `y` .

Description

vsErfInv vdErfInv vmsErfInv vmdErfInv

The ErfInv function computes the inverse error function values for elements of the input vector a and writes them to the output vector y

y = erf^{-1}(a) ,

where erf(x) is the error function defined as given by:

Useful relations:

where erfc is the complementary error function.

where

is the cumulative normal distribution function.

where Φ^{-1}(x) and erf^{-1}(x) are the inverses to Φ(x) and erf(x) respectively.

Figure “ErfInv Family Functions Relationship” illustrates the relationships among ErfInv family functions ( ErfInv , ErfcInv , CdfNormInv ).

ErfInv Family Functions Relationship

Sparse Matrices That Can be Solved With PARDISO

Useful relations for these functions:

Special Values for Real Function v?ErfInv(x)

Argument	Result	VM Error Status	Exception
+0	+0
-0	-0
+1	∞	VML_STATUS_SING	ZERODIVIDE
-1	∞	VML_STATUS_SING	ZERODIVIDE
`\(\|X\| > 1\)`	QNAN	VML_STATUS_ERRDOM	INVALID
∞	QNAN	VML_STATUS_ERRDOM	INVALID
∞	QNAN	VML_STATUS_ERRDOM	INVALID
QNAN	QNAN
SNAN	QNAN		INVALID

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

v?ErfInv

Syntax

Include Files

Input Parameters

Output Parameters

Description

ErfInv Family Functions Relationship